The present invention relates to a grounded inductance circuit and an LC resonance circuit utilizing a gyrator circuit and specifically relates to an LC resonance circuit frequency-stabilized against a temperature change.
In the fields of electronic circuits including ICs, a variety of attempts have been made recently to incorporate into an IC electronic parts which have been arranged conventionally on the periphery of the IC.
In particular, it has been presumed as advantageous to provide an inductance element in the interior of the IC, because a major area of the LC resonance circuit is occupied by the inductance element and because a degree of freedom to specify the characteristic of the inductance element is limited.
As a method of providing an inductance in an interior of an IC, the method has been reported in which an ac-equivalent inductance is formed utilizing a gyrator circuit.
FIG. 1 represents a circuit diagram to illustrate the principle of a conventional gyrator circuit.
As is shown in the figure, the gyrator circuit is made up of first and second operational transconductance amplifiers, OTA 1 and OTA 2 with the differential output terminals C,D of OTA 1 connected to the differential input terminals S,T of OTA 2, respectively, and with the differential output terminals E,F of OTA 2 cross-connected to the differential input terminals B, A of OTA 1, respectively. In addition, a capacitor C.sub.1 is connected between the differential output terminals C, D of OTA 1.
FIG. 2 is a block diagram of an ac-equivalent circuit of the gyrator circuit shown in FIG. 1.
In FIG. 1 and FIG. 2, I' and V' denote ac components of a current I and a voltage V, respectively.
The ac current I.sub.1 ' flows through the current path in OTA 2 the conductance of which is controlled by the base voltage V.sub.2 ' of OTA 2 produced across capacitor C.sub.1.
Accordingly, it follows that EQU I.sub.1 '=G.sub.2 V.sub.2 ', (1)
wherein G.sub.2 stands for the transconductance of OTA 2.
Similarly, EQU -I.sub.2 '=G.sub.1 V'.sub.1, (2)
wherein G.sub.1 stands for the transconductance of OTA 1.
Substituting V.sub.2 ' with -I.sub.2 '/(jC.sub.1 .omega.) and eliminating I.sub.2 ' from equations (1) and (2) yield EQU V'.sub.1 /I'.sub.1 =j.omega.[C.sub.1 /(G.sub.1 G.sub.2)] (3)
Putting EQU L=C.sub.1 /(G.sub.1 G.sub.2) (4)
gives ##EQU1##
If the transconductance of OTA 1 equals the transconductance of OTA 2, i.e., G.sub.1 =G.sub.2, then EQU L=C.sub.1 R.sub.g.sup.2, (6)
wherein R.sub.g denotes the impedance of each of the OTAs.
FIG. 3 is a circuit diagram of an OTA practically used in a gyrator circuit.
As is shown in the figure, each of the differential inputs is connected to the bases of a couple of NPN transistors (Q1,Q2), (Q3,Q4), wherein transistors Q1 and Q4 make up a differential amplifier and transistors Q2 and Q3 make up another differential amplifier.
In FIG. 3, the symbol xn stands for an emitter area n times as large as the emitter area of the transistor not affixed with the symbol. The transistors not affixed with the symbol have the same emitter area as each other. The preferable value of n is 4.
The constant current source denoted by S3 supplies a carrier of I.sub.g to the emitters of transistors Q1,Q4 of the first differential amplifier, and the constant current source S4 supplies carrier of the same intensity I.sub.g to the emitters of transistors Q2,Q3 of the second differential amplifier. Through current loads L1 and L2 constant currents of the same intensity I.sub.g flow.
This circuit structure of the OTA is intended to extend the dynamic range of the OTA.
Now, let collector currents of transistors Q1, Q2, Q3 and Q4 be I.sub.1, I.sub.2,I.sub.3 and I.sub.4 respectively.
Then, EQU I.sub.1 +I.sub.2 =I.sub.g +I.sub.o, (7) EQU I.sub.3 +I.sub.4 =I.sub.g -I.sub.o, (7' ) ##EQU2## EQU I.sub.1 =n.multidot.I.sub.s exp [V.sub.BE1 /V.sub.T ], (9) EQU I.sub.2 =I.sub.s exp [V.sub.BE2 /V.sub.T ], (9') EQU I.sub.3 =n.multidot.I.sub.s exp [V.sub.BE3 /V.sub.T ], (10) EQU I.sub.4 =n.multidot.I.sub.s exp [V.sub.BE4 /V.sub.T ], (10')
Thus, EQU I.sub.1 /I.sub.4 =n.multidot.exp [V.sub.d /V.sub.T ], (11) EQU I.sub.2 /I.sub.3 =n.sup.-1 .multidot.exp [V.sub.d /V.sub.T ], (11')
wherein V.sub.d represents the differential input voltage, V.sub.BE1 and V.sub.BE2, V.sub.BE3 and V.sub.BE4 representing the base-emitter voltages of transistors Q1, Q2, Q3 and Q4 respectively, I.sub.s denoting the reverse saturation current, and V.sub.T denoting the thermal voltage, i.e., kT/q.
Eliminating the variables except for I.sub.0, I.sub.g and V.sub.d from equations (7) to (11') leads to the equation ##EQU3## Now, we express equation (12) in power series of V.sub.d and ignore the higher order terms. Then, EQU I.sub.o =[I.sub.o ].sub.Vd=0 +[.delta.I.sub.o /.delta.V.sub.d ].sub.Vd=0 V.sub.d. (13)
Since [.delta.I.sub.o /.delta.V.sub.d ].sub.Vd=0 is a transconductance G by definition, and [I.sub.o ].sub.Vd=0 =0, it follows that EQU I.sub.o =GV.sub.d, (14)
wherein EQU G=[n/(1+n).sup.2 ].multidot.(I.sub.g /V.sub.T) (15)
The above argument holds in each of the two OTAs which make up a gyrator circuit.
FIG. 4 is a circuit diagram of a resonance circuit utilizing the gyrator circuit made up of OTAs as shown in FIG. 3.
Like the gyrator circuit illustrated in FIG. 1, a first output terminal C and a second output terminal D of OTA 1 are connected to the first input terminal connected to the bases of the transistors Q13 and Q14 and the second input terminal connected to the bases of the transistors Q15 and Q16, respectively, of OTA 2, while a first output terminal E and a second output terminal F of OTA 2 are connected to the second input terminal connected to the bases of transistors Q7 and Q8 and the first input terminal connected to the bases of transistors Q5 and Q6, respectively, of OTA 1. In addition, a stabilized dc voltage VS1 is applied between the second input terminal Q of OTA 1 and the ground potential in order to effect ac-grounding of one end of the gyrator inductance, causing the first output terminal E of OTA2 to be kept at a constant voltage VS1.
In the figure, the symbol x4 represents a transistor having an emitter area four times as large as the emitter area of a transistor not affixed with the symbol, as described above.
A capacitor C3 for parallel resonance is connected between an ac signal source and the ground potential. Another capacitor C2 for series resonance is connected between the signal source and the input terminal of OTA 1 through resistor R1. The resistor R1 is provided to lower the Q of the resonance circuit.
A stabilized current supply SCS is provided for supplying constant currents I.sub.g through current mirror circuits to the current sources made of NPN transistors Q9, Q10 of OTA 1 and NPN transistors Q17, Q18 of OTA2, and for supplying constant currents I.sub.g to the PNP load transistors Q11, Q12 of OTA1 and Q19, Q20 of OTA2.
The stabilized current supply is made up of serially connected PNP and NPN transistors, Q3, Q1, respectively, serially connected PNP and NPN transistors, Q4, Q2, respectively, dc voltage source VS2, and a current-regulating register R2.
The emitter of transistor Q3 is connected to a positive electrode of dc voltage source VS2, and the emitter of transistor Q1 is connected to the grounded negative electrode of the dc voltage source VS2, thereby making up a current generating circuit. Transistor Q1 is diode connected, the base of which is connected to the base of transistor Q2 to constitute a current mirror circuit.
The serially connected transistors Q2 and Q4 make up an output circuit of the current mirror circuit with the diode-connected transistor Q4 acting as a load transistor. The collector of the load transistor Q4 is connected to the base of the transistor Q3 to form a negative-feedback signal path to stabilize the current I.sub.c flowing through the collectors of transistors Q2 and Q4. The current intensity is determined depending on the value of the resistor R2.
The base line connected with the bases of transistor Q1 and Q2 is connected to the bases of transistors Q9, Q10, Q17 and Q18 to form a current mirror circuit to transfer the current to the current-source transistors (Q9, Q10, Q17, Q18) of OTA 1 and OTA 2.
The base line connected with the bases of transistors Q3 and Q4 is connected to the bases of the transistors Q11, Q12, Q19 and Q20 to form another current mirror circuit for transferring the current to the current load transistors (Q11, Q12. Q19, Q20) of OTA 1 and OTA 2.
The operation of the gyrator circuit shown in FIG. 4 will next be described.
As described in equation (14), the output current of OTA 1 and OTA 2 are given by EQU I.sub.o1 =G.sub.1 V.sub.d1, (16) EQU I.sub.o2 =G.sub.2 V.sub.d2, (17)
wherein the suffixes 1 and 2 refer to quantities relating to OTA 1 and OTA 2, respectively, and EQU V.sub.d1 =V.sub.p -V.sub.q, (18) EQU V.sub.d2 =V.sub.r -V.sub.s, (19)
V.sub.p and V.sub.q denoting electric potentials at the first and second input terminals P and Q, respectively, of OTA 1, and V.sub.r and V.sub.s denoting electric potentials at the first and second input terminals R and S, respectively, of OTA 2.
It is to be noted that the positive sign of the output current I.sub.o corresponds to the direction of the current which flows toward the first output terminal from the second output terminal, as described in FIG. 3.
Let the impedance of the capacitor C1 be z, then ##EQU4##
Substituting equation (20) into equation (17) yields EQU I.sub.o2 =G.sub.1 G.sub.2 z.multidot.V.sub.d1. (21)
In case that z=1/(jC.omega.), ##EQU5## which agrees with equation (3).
FIG. 5 represents a temperature dependence of the input impedance of the gyrator circuit shown in FIG. 4 plotted against frequency.
The figure shows that the temperature variation from -10.degree. C. to 50.degree. C. causes a shift of the impedance characteristic by 30K Hz, i.e., .+-.15 KHz with respect to the center frequency of 450 KHz.
This undesirable shift of the input impedance entails a fluctuation of the resonance frequency by .+-.15 KHz for the same temperature variation.
The frequency variation versus a temperature variation of an ordinary resonance circuit in which a ceramic element is employed as a capacitor element is approximately .+-.1.5 KHz for the above-described range of temperature variation.
For this reason, the temperature dependence of the resonance circuit utilizing the prior art gyrator circuit is ten times as large as that of an ordinary resonance circuit.
In FIG. 4, main dc biases are entered which are simulated by means of the circuit simulator of Spice et al. The simulation was implemented under the following conditions: temperature 25.degree. C.; series resonance frequency 410 KHz; parallel resonance frequency 490 KHz; center frequency 450 KHz; input impedance 11 K.OMEGA. at 450 KHz; tension of dc voltage source VS2 1.05 V; and ac ground potential 860 mV. In addition, the simulation is performed assuming that the temperature characteristics of the dc voltage source VS2 and the ac ground potential are the same as the temperature characteristic of V.sub.BE of transistors used in order to take the temperature characteristic of the V.sub.BE of the transistor out of consideration.
From the result of the simulation above, it is known that the biases of input and output terminals of the OTAs significantly deviate from their normal values, causing the transistors to saturate and thereby interrupting the transistors normally to work. Furthermore, it is known that the phase of the input impedance of the resonance circuit of FIG. 4 is approximately 37 degrees in contrast to the normal value of 90 degrees.
It is an object of the present invention to provide a grounded inductance circuit and LC resonance circuit utilizing a gyrator circuit of a stable frequency characteristic, in which the dc biases will not deviate from the normal values and the series and parallel resonance frequencies will not be influenced by a temperature variation.